The necessity for modified check valve designs (e.g., as described herein and in related patents) may be better appreciated after first considering: (1) the remarkably high failure rates of conventional reciprocating high-pressure pumps (especially their fluid ends), and (2) the substantial uncertainties (e.g., in cost/benefit analysis and technical complexity/reproducibility) associated with multistage well stimulation in unconventional formations. Pump-related issues will be considered initially.
Frac pumps (also commonly called fracking or well-service pumps) are typically truck-mounted for easy relocation from well-to-well. And they are usually designed in two sections: the (proximal) power section (herein “power end”) and the (distal) fluid section (herein “fluid end”). Each pump fluid end comprises at least one subassembly, and commonly three or more, in a single fluid end housing. Each subassembly comprises a suction valve, a discharge valve, a plunger or piston, and a portion of (or substantially the entirety of) a pump fluid end subassembly housing (shortened herein to “pump housing” or “fluid end housing” or “housing”, depending on the context).
For each pump fluid end subassembly, its fluid end housing comprises a pumping chamber in fluid communication with a suction bore, a discharge bore, and a piston/plunger bore. A suction valve (i.e., a check valve) within the suction bore, together with a discharge valve (i.e., another check valve) within the discharge bore, control bulk fluid movement from suction bore to discharge bore via the pumping chamber. Note that the term “check valve” as used herein refers to a valve in which a (relatively movable) valve body can cyclically close upon a (relatively stationary) valve seat to achieve substantially unidirectional bulk fluid flow through the valve.
Pulsatile fluid flow results from cyclical pressurization of the pumping chamber by reciprocating plunger or piston strokes within the plunger/piston bore. Suction and pressure strokes alternately produce wide pressure swings in the pumping chamber (and across the suction and discharge check valves) as the reciprocating plunger or piston is driven by the pump power end.
Such pumps are rated at peak pumped-fluid pressures in current practice up to about 22,000 psi, while simultaneously being weight-limited due to the carrying capacity of the trucks on which they are mounted. (See, e.g., U.S. Pat. No. 7,513,759 B1, incorporated by reference).
Due to high peak pumped-fluid pressures, suction check valves experience particularly wide pressure variations between a suction stroke, when the valve opens, and a pressure stroke, when the valve closes. For example, during a pressure stroke with a rod load up to 350,000 pounds, a conventionally rigid/heavy check valve body may be driven longitudinally (by pressurized fluid behind it) toward metal-to-metal impact on a conventional frusto-conical valve seat at closing forces of about 50,000 to over 250,000 pounds (depending on valve dimensions). A portion of total check-valve closure impulse energy (i.e., the total kinetic energy of the moving valve body and fluid at valve seat impact) is thus converted to a short-duration high-amplitude valve-closure energy impulse (i.e., a mechanical shock). As described below, each such mechanical shock is associated with transmission of broad-spectrum vibration energy, the range of vibration spectrum frequencies being an inverse function of valve-closure energy impulse duration.
Repeated application of dual valve-closure shocks with each pump cycle (i.e., one shock from the suction valve and another shock from the discharge valve) predisposes each check valve, and the pump as a whole, to vibration-induced (e.g., fatigue) damage. (Recall the well-documented progressive cracking of the Liberty Bell with repeated strikes of the clapper, particularly noting the sites of crack progression being significantly distant from the sites of clapper impact). Thus, cumulative valve-closure shocks significantly degrade frac pump reliability, proportional in part to the rigidity and weight of each check valve body.
The increasing importance of fatigue-related frac pump reliability issues has paralleled the inexorable rise of peak pumped-fluid pressures in new fracking applications. And insight into fatigue-related failure modes has been gained through review of earlier shock and vibration studies, data from which are cited herein. For example, a recent treatise on the subject describes a mechanical shock in terms of its inherent properties in the time domain and in the frequency domain, and also in terms of its effects on structures when the shock acts as the excitation. (see p. 20.5 of Harris' Shock and Vibration Handbook, Sixth Edition, ed. Allan G. Piersol and Thomas L. Paez, McGraw Hill (2010), hereinafter Harris).
References to time and frequency domains appear frequently in descriptions of acquisition and analysis of shock and vibration data. And these domains are mathematically represented on opposite sides of equations generally termed Fourier transforms. Further, estimates of a shock's structural effects are frequently described in terms of two parameters: (1) the structure's undamped natural frequency and (2) the fraction of critical structural damping or, equivalently, the resonant gain Q (see Harris pp. 7.6, 14.9-14.10, 20.10). (See also, e.g., U.S. Pat. No. 7,859,733 B2, incorporated by reference).
Digital representations of time and frequency domain data play important roles in computer-assisted shock and vibration studies. In addition, shock properties are also commonly represented graphically as time domain impulse plots (e.g., acceleration vs. time) and frequency domain vibration plots (e.g., spectrum amplitude vs. frequency). Such graphical presentations readily illustrate the shock effects of metal-to-metal valve-closure, wherein movement of a check valve body is abruptly stopped by a valve seat. Relatively high acceleration values and broad vibration spectra are prominent, because each valve-closure impulse response primarily represents a violent conversion of a portion of kinetic energy (of the moving valve body and fluid) to other energy forms.
Since energy cannot be destroyed, and since a conventional valve can neither store nor convert (i.e., dissipate) more than a small fraction of the valve-closure impulse's kinetic energy, a portion of that energy is necessarily transmitted to the pump housing in the form of broad-spectrum vibration energy. This relationship of (frequency domain) vibration energy to (time domain) kinetic energy, is mathematically represented by a Fourier transform. Such transforms are well-known to those skilled in the art of shock and vibration mechanics. For others, a graphical representation (i.e., plots) rather than a mathematical representation (i.e., equations) may be preferable.
For example, in a time domain plot, the transmitted energy appears as a high-amplitude impulse of short duration. And a corresponding frequency domain plot of transmitted energy reveals a relatively broad-spectrum band of high-amplitude vibration. ***The breadth of the vibration spectrum is generally inversely proportional to the impulse duration.***
Thus, as noted above, a portion of the check valve's cyclical valve-closure kinetic energy is converted to relatively broad-spectrum vibration energy. The overall effect of cyclical check valve closures may therefore be compared to the mechanical shocks that would result from repeatedly striking the valve seat with a commercially-available impulse hammer, each hammer strike being followed by a rebound. Such hammers are easily configured to produce relatively broad-spectrum high-amplitude excitation (i.e., vibration) in an object struck by the hammer. (See, e.g., Introduction to Impulse Hammers at http://www.dytran.com/img/tech/a11.pdf, and Harris p. 20.10).
Summarizing then, relatively broad-spectrum high-amplitude vibration predictably results from a typical high-energy valve-closure impulse. And frac pumps with conventionally-rigid valves can suffer hundreds of these impulses per minute. Note that the number of impulses per minute (for example, 300 impulses per minute) corresponds to pump plunger strokes or cycles, and this number may be converted to impulses-per-second (i.e., 300/60=5). In this example, the number 5 is sometimes termed a frequency because it is given the dimensions of cycles/second or Hertz (Hz). But the “frequency” thus attributed to pump cycles themselves differs from the spectrum of vibration frequencies resulting from each individual pump cycle energy impulse. The difference is that impulse-generated (e.g., valve-generated) vibration occurs in bursts having relatively broad spectra (i.e., simultaneously containing many vibration frequencies) ranging from a few Hz to several thousand Hz (kHz).
In conventional frac pumps, nearly all of the (relatively broad-spectrum) valve-generated vibration energy must be transmitted to proximate areas of the fluid end or pump housing because vibration energy cannot be efficiently dissipated in the (relatively rigid) valves themselves. Based on extensive shock and vibration test data (see Harris) it can be expected to excite damaging resonances that predispose the housing to fatigue failures. (See, e.g., U.S. Pat. No. 5,979,242, incorporated by reference). If, as expected, a natural vibration resonance frequency of the housing coincides with a frequency within the valve-closure vibration spectrum, fluid end vibration amplitude may be substantially increased and the corresponding vibration fatigue damage made much worse. (See Harris, p. 1.3).
Opportunities to limit fluid end damage can reasonably begin with experiment-based redesign to control vibration-induced fatigue. That is, spectra of the equipment vibration frequencies measured after application of test shocks can reveal structural resonance frequencies likely to cause trouble in a particular fluid end. These revealed frequencies are herein termed critical frequencies. For example, a test shock may comprise a half-sine impulse of duration one millisecond, which has predominant spectral content up to about 2 kHz (see Harris, p. 11.22). This spectral content likely overlaps, and thus will excite, a plurality of a fluid end's structural resonance (i.e., critical) frequencies. Excited critical frequencies are then identified with appropriate instrumentation, so attention can be directed to limiting operational vibration at those critical frequencies. This process is tailored to each fluid end, with an appropriate test shock and instrumentation to provide at least one “tested fluid end vibration resonant frequency” to support further reliability improvements.
Limiting vibration at critical frequencies through use of the above shock tests can be particularly beneficial in blocking progressive fatigue cracking in a structure. If vibration is not appropriately limited, fatigue cracks may grow to a point where fatigue crack size is no longer limited (i.e., the structure experiences catastrophic fracture). The size of cracks just before the point of fracture has been termed the critical crack size. Note that stronger housings are not necessarily better in such cases, since increasing the housing's yield strength causes a corresponding decrease in critical crack size (with consequent earlier progression to catastrophic fracture). (See Harris, p. 33.23).
It might be assumed that certain valve redesigns proposed in the past (including relatively lighter valve bodies) would have alleviated at least some of the above fatigue-related failure modes. (See, e.g., U.S. Pat. No. 7,222,837 B1, incorporated by reference). But such redesigns emerged (e.g., in 2005) when fluid end peak pressures were generally substantially lower than they currently are. In relatively lower pressure applications (e.g., mud pumps), rigid/heavy valve bodies performed well because the valve-closure shocks and associated valve-generated vibration were less severe compared to shock and vibration experienced more recently in higher pressure applications (e.g., fracking). Thus, despite their apparent functional resemblance to impulse hammers, relatively rigid/heavy valves have been pressed into service as candidates for use in frac pump fluid ends. Indeed, they have generally been among the valves most commonly available in commercial quantities during the recent explosive expansion of well-service fracking operations. Substantially increased fluid end failure rates (due, e.g., to cracks near a suction valve seat deck) have been among the unfortunate, and unintended, consequences.
Under these circumstances, it is regrettable but understandable that published data on a modern 9-ton, 3000-hp well-service pump includes a warranty period measured in hours, with no warranty for valves or weld-repaired fluid ends.
Such baleful vibration-related results in fluid ends might usefully be compared with vibration-related problems seen during the transition from slow-turning two-cylinder automobile engines to higher-speed and higher-powered inline six-cylinder engines around the years 1903-1910. Important torsional-vibration failure modes suddenly became evident in the new six-cylinder engines, though they were neither anticipated nor understood at the time. Whereas the earlier engines had been under-powered but relatively reliable, torsional crankshaft vibrations in the six-cylinder engines caused objectionable noise (“octaves of chatter from the quivering crankshaft”) and unexpected catastrophic failures (e.g., broken crankshafts). (Quotation cited on p. 13 of Royce and the Vibration Damper, Rolls-Royce Heritage Trust, 2003). Torsional-vibration was eventually identified as the culprit and, though never entirely eliminated, was finally reduced to a relatively minor maintenance issue after several crankshaft redesigns and the development of crankshaft vibration dampers pioneered by Royce and Lanchester.
Reducing the current fluid end failure rates related to valve-generated vibration in frac pumps requires an analogous modern program of intensive study and specific design changes. The problem will be persistent because repeatedly-applied valve-closure energy impulses cannot be entirely eliminated in check-valve-based fluid end technology. So the valve-closing impulses must be modified, and their associated vibrations damped, meaning that at least a portion of the total vibration energy is converted to heat energy and dissipated (i.e., the heat is rejected to the surroundings). A reduction in total vibration energy results in reduced excitation of destructive resonances in valves, pump housings, and related fluid end structures.